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The problem offers opportunities to think about area, proportion and fractions, while offering an informal introduction to the mathematics of infinity and convergence which would not normally be met by younger students, to tempt their curiosity.
Show the first image from the problem for a short while and invite students to look at it in silence. Then hide the image and give them some time to reflect on what they saw and then discuss with a partner, and finally share with the whole class.
In the Teachers' Resources to Inside Seven Squares there is a demonstration of how paper folding could be used to help students to create the shapes, and see the relationship between areas.
Vanishing Point uses the same starting point and goes on to explore the question of continuing the sequence indefinitely.